How do astronomers determine stellar parallax?

Question

Asher Cohen · Accepted Answer

By measuring parallax using sophisticated instruments.

Astronomers use an effect called parallax to measure distances to nearby stars. Parallax is the apparent displacement of an object because of a change in the observer's point of view. For this, the observer moves between the two positions to view same object, between, object would appear to move against the background.

Taken from here.

For measuring a star's distance using sophisticated instruments, astronomers position it once, and then again 6 months later (against far more distant stars), when earth has moved on the opposite side of its orbit and calculate the apparent change in position. See figure below.

The star's apparent motion is called stellar parallax. The distance #d# is measured in parsecs and the parallax angle #p# is measured in arc seconds.

It is apparent that #d=1/p#.

So a distance of one parsec is one at which earth's orbit subtends an angle of one arc second and distance of two parsecs is one at which earth's orbit subtends an angle of half of an arc second. A parsec is equal to about 3.26 light-years

Levi Anderson · Answer

Imagine that you observe the star twice in an interval of half a year. The angle between the directions is the star parallax.

It is convenient to select diametrically opposite positions within Earth's orbit; however, the closer the positions, the more precise the instrument must be. For this selection, the observer's in-between distance falls between 1.991 AU and 2 AU; if equinoxes are selected, the in-between distance between Earth's orbital positions will be very near to 2 AU. Explanation: Using the parallax isosceles triangle, we can obtain the following formulas: distance from the observer = cosec (parallax/2) = 515662 AU = 8.3 ly; the difference is very small. If the parallax angle is 0.8", the star distance in AU from the Sun is cot (parallax/2) = cot (.4") = 515662 AU = 8.2 ly, nearly.

Ivy Allen · Answer

undefined By measuring the apparent shift in a nearby star's position relative to the background of more distant stars as Earth orbits the Sun, astronomers can determine stellar parallax. This shift results from a change in the viewing angle from opposite sides of Earth's orbit, and by measuring the angle of this shift, astronomers can use trigonometry to calculate the star's distance, with the baseline of Earth's orbit acting as one side of the triangle and the observed shift as the other.